Assessment of common hyperelastic constitutive equations for describing normal and osteoarthritic articular cartilage

Abstract

With the aim of providing information for modelling joint and limb systems, widely available constitutive hyperelastic laws are evaluated in this paper for their ability to predict the mechanical responses of normal and osteoarthritic articular cartilage. Load-displacement data from mechanical indentation were obtained for normal and osteoarthritic cartilage at 0.1 s(-1) and 0.025 s(-1) and converted to the stress-stretch ratio. The data were then fitted to the Arruda-Boyce, Mooney-Rivlin, neo-Hookean, Ogden, polynomial, and Yeoh hyperelastic laws in the MATLAB environment. Although each of the hyperelastic laws performed satisfactorily at the higher rate of loading, their ability to fit experimental data at the lower loading rate varied considerably. For the preferred models, coefficients were provided for stiff, soft, and average tissues to represent normal and degraded tissue at high and low loading rates. The present authors recommend the use of the Mooney-Rivlin or the Yeoh models for describing both normal and degraded articular cartilage, with the Mooney-Rivlin model providing the best compromise between accuracy and required computational power.

Microscale consolidation analysis of relaxation behavior of single living chondrocytes subjected to varying strain-rates

“…For simplicity, the neo-Hookean strain energy density function was used in this study (Brown et al, 2009;ABAQUS, 1996) as follows:…”

Stress profile of infant rib in the setting of child abuse: A finite element parametric study

“…Additional data regarding the stress-strain response of infant rib bone are required before these constitutive models can be used in the FE analysis. Similarly, adult cartilage is typically characterized as viscoelastic and hyperelastic (Brown et al, 2009;Lu and Mow, 2008;Natali and Meroi, 1990), and the use of a linear elastic model in this study is likely a simplification of the real material. Despite this limitation, the sensitivity analysis found cartilage properties significantly affect the stress in the rib, supporting the need to get accurate material properties in both bone and cartilage before predictions of infant rib fracture can be made.…”

Evaluation of hyperelastic models for the non-linear and non-uniform high strain-rate mechanics of tibial cartilage

“…Cartilage behaves as a nearly incompressible material under high strain-rates (Wong et al, 2000) and is frequently modeled as incompressible (Ateshian et al, 2007;Brown et al, 2009;Mow et al, 1980). For unconfined compression of an incompressible material, employing the Padé approximation of the inverse Langevin (Cohen, 1991), the nominal stress in the axial direction becomes (Arruda and Boyce, 1993): where λ is the applied axial stretch and λ chain ¼ ðλ 2 þ 2=λÞ=3 Â Ã 1=2 .…”

“…Since the driver of knee AC short-term response, the collagen network, can be analogized to a statistical chain network, these models are strong candidates for modeling the short-term response of AC (Brown et al, 2009). However, the ability of the model to replicate the high strain-rates associated with walking or the non-uniform mechanical properties of tibial AC remains unknown.…”